VEACH, TEXAS. Veach is on a country road just west of Farm Road 705 twenty-one miles south of San Augustine in southern San Augustine County. It was named for John A. Veach, an early settler, and received a post office in 1916. The post office was closed in the 1930s, and in 1940 Veach had twenty inhabitants, one business, and scattered dwellings. In the 1980s the community still had a number of dwellings.